Here's a homework question in Abstract Algebra that I have some troubles solving.
Given that permutation $\sigma=(1 2 4)(1 5 2)$, and $\sigma\subset A_5$. Find the number of right cosets of the cyclic subgroup $<\sigma>$ in $A_5$.
I think permutation $\sigma=(1 2 4)(1 5 2)$ can be written as $(1 5 4)$, but I'm having trouble seeing the cyclic subgroup $<(1 5 4)>$ in $A_5$, and also the right cosets of cyclic subgroup in this case.
Does it have something to do with the length of the cyclic subgroup? Thanks.